Great question, Thomas! For me personally, I'd say my accent (Standard American/born and raised in California) stays consistent when I sing. But I will change pronunciation (especially vowel shapes) depending on the style. So Adele, for example, uses a lot of dark, rounded vowels - and I may incorporate some of those, while not trying to imitate her accent. Some genres (country, for example) bring out a stronger accent as part of the style.